To move in a misdirected yet very purposeful manner, usually making a big scene and calling lots of attention to oneself in the process. It can be wandering aimlessly or striding very purposefully toward someone/something but with lots of distractions along the way and always completely ignorant of everything going on around oneself.
In short, a sort of all-over-the-place reckless abandon where you're either totally focused on something, or not focused on anything at all, but completely ignoring everyone around you as you knock into things, walk this way and that as if you forgot where you wanted to go next, and in general making a complete spectacle of yourself.
The loud, fat old woman with the voluminous flowered blouse and garish tri-coloured shawl went blumbing through the entire marketplace, upsetting EVERYTHING in her path.
The nosy neighbour woman blumbled down the lane, looking for her twelve cats.